If you are part way through a process, and that process has fidelity, you are aware of the stage you are up to, relative to the stages that have developed (in principle).
No, I don't think so. And, if you consider it just for a moment, you shouldn't either.
The problems here are scale, expectations and experience.
Let's use another "process" as an example: aging.
You are, at any single conscious moment, aware of your physical existence.
You have experience/memory of previous stages of your existence, when you were younger.
You have some, more or less reasonable, expectations about future stages of your existence, based on observations of others.
But this "awareness" is extremely limited, even faulty.
Your memory is not perfect, often it is even wrong. You have a recollection - more of a reconstruction - of how you were in the past... but it isn't an "awareness".
Your understanding of your present stage is limited by the amount of change that you can distinguish. In the time it took for you to read this post, you have aged. I would bet that you are not aware of any difference in age between
now and
5 minutes earlier.
You expectations of your future self are necessarily based on external observations. They obviously cannot be based on your own awareness.
So, here we have it: you are "part way through a process", the process "has fidelity"... and your awareness of the stage you are at is extremely limited.
Now that process - "aging" - is a process where you, the individual, are constantly and continuously involved.
But Evolution works differently. Evolution as a process is disconnected from the individual. You have been told that before, often, even in this thread:
individuals do not 'evolve' - species/genetic lines do.
So the "previous state" in the process of evolution is not you. It is someone else. An ancestor of yours.
The "future state" in this process is not you either. It is your descendants.